Session K02: Ferroic Order and Multipole

Linear electro-optic effect in trigonal LiNbO3: a first-principles study

Lithium niobate LiNbO₃ (LN) has emerged as a promising electro-optic material with applications in silicon photonics. It demonstrates a fairly large linear electro-optic response, often referred to as a Pockels effect. In this talk, we report a first-principles investigation of the origins of the Pockels response in ferroelectric R3c LN. We examine three contributions to the Pockels tensor, its electronic, ionic (Raman), and piezoelectric components. Unlike the BaTiO₃ case, where the Pockels response primarily arises from very low phonon frequencies, the Raman susceptibility terms can be attributed to specific A₁ modes that have a significant impact on the Nb-O bonding length. We compare our Raman susceptibility results obtained from the finite difference method and the density functional perturbation theory. To examine the origin of the piezoelectric Pockels response, we compute the elasto-optic and piezoelectric tensors. Importantly, the largest component of the Pockels tensor r₃₃ is dominated by the ionic response, which explains a relatively weak frequency dependence of the EO effect in LN.   

Direct observation of strain-induced ferrochiral transition in quasi-1D BaTiS3

Ferroaxial order is a relatively underexplored phenomenon that is characterized by a rotational structural distortion with an axial vector symmetry. The symmetry requirement for a ferroaxial transition is broken mirror symmetry in a plane parallel to the rotation axis. Ferroaxial order when coupled with ferroelectric order — that is characterized by the breaking of inversion symmetry — can lead to ferrochiral materials that combine chirality with electric polarization. Ferrochiral materials are rare. Here, we report direct observation of a strain-induced ferrochiral transition in a single crystal of a quasi-one-dimensional chalcogenide, BaTiS₃. Using a combination of aberration-corrected scanning transmission electron microscope (STEM) imaging and density-functional-theory (DFT) calculations, we show that biaxial strain along ab-plane perpendicular to the 1D chains of TiS₆ octahedra in BaTiS₃ transforms it from a higher symmetry phase with P6₃cm space group to a ferrochiral P6₃ phase. The ferrochiral phase is characterized by a rotational distortion of the TiS₆ octahedra along the axis containing the chains, and polarization along the chain direction. We also show direct observation of the ferrochiral domains and domain walls with atomic resolution. Finally, using phenomenological modeling, we propose that the chirality can be switched with an external electric field.   

Measurement of ferroaxial moments via piezoresistivity

There has been recent interest in electronic states with unusual combinations of spatial and time-reversal symmetry breakings. One such example are ferroaxial phases, which are described by dipolar electric toroidal moments whose condensation preserves inversion and time-reversal, breaking only mirror symmetries. Detection of ferroaxial order, however, has been difficult as the order parameter does not couple directly to electric or magnetic fields. Using representation theory, we determine all tensors that share an irreducible representation with the ferroaxial moment and hence can be used to directly detect it. Searching through materials databases, we identify a list of existing candidate materials that exhibit ferroaxial order as their primary order parameter across a phase transition. Focusing on the piezoresistivity, we use first-principles density functional theory to demonstrate that certain off-diagonal elements of the response tensor become non-zero only in the ferroaxial phase of the double perovskite fluorite CaSnF6.   

Quantum fluctuation of ferroelectric order in polar metals

The polar metallic phase is an unusual metallic phase of matter containing long-range ferroelectric (FE) order in the electronic and atomic structure. Distinct from the typical FE insulating phase, this phase spontaneously breaks the inversion symmetry without global polarization. Unexpectedly, the FE order is found to be dramatically suppressed and destroyed at moderate ~10% carrier density. Here, we propose a general mechanism based on carrier-induced quantum fluctuations to explain this puzzling phenomenon. The quantum kinetic effect would drive the formation of polaronic quasi-particles made of the carriers and their surrounding dipoles. The disruption in dipolar directions can therefore weaken or even destroy the FE order. We demonstrate such polaron formation and the associated FE suppression via a concise model using exact diagonalization, perturbation, and quantum Monte Carlo approaches. This quantum mechanism also provides an intuitive picture for many puzzling experimental findings, thereby facilitating new designs of multifunctional FE electronic devices augmented with quantum effects.   

Phonon-mediated spin Hall effect in quantum paraelectric metals

Recent years have seen discovery of ferroelectric phase transition in various metallic materials. Given that incipient ferroelectricity usually implies the crystal near continuous phase transition, its existence in metals with spin-orbit coupling typically gives rise to soft transverse optical phonons with Rashba-type coupling to itinerant electrons. We find through the Kubo formula calculation that such Rashba electron-phonon coupling has a profound impact on electron spin transport. While finite polarity is required for spin Hall current induced by uniform electric field, the Rashba electron-phonon coupling is sufficient for giving rise to spin Hall current proportional to a second derivative of electric field with distinct quadrupolar characteristics. Furthermore, this spin conductivity displays an unusual thermal activation behavior characterized by a scaling laws dependent on the phonon frequency to temperature ratio. These findings shed light on exotic electronic transport phenomena originating from ferroelectric quantum criticality, highlighting the intricate interplay of charge and spin degrees of freedom.   

Polarization in inhomogeneous crystals and its relationship to quadrupole moments

The formulae for polarization and orbital magnetization in crystals are expressed in terms of the Bloch wavefunctions and they are closely related to Berry curvature. As a result, their properties as bulk quantities are well established. In contrast, definitions of higher-order electric/magnetic multipole moments in crystals as bulk quantities are still elusive. We revisit this problem by considering the polarization in inhomogeneous crystals. While it has been calculated by semiclassical theory in a previous work (Y. Zhang, Y. Gao, D. Xiao, Phys. Rev. B 104, 144203 (2021)), in the present work, we calculate it by linear response theory and compare it with previous works. Since such polarization is expected to be equal to a gradient of the quadrupole moment, we define the electric quadrupole moment from this result, and discuss its properties, including its relationship to polarizability. Orbital magnetic quadrupole moments are also discussed along the same line.   

Nuclear Boost to Pseudomagnetic Fields from Quantum Geometry

Recent experiments demonstrate precise control over coherently excited phonon modes using high-intensity terahertz lasers, opening new pathways towards dynamical, ultrafast design of magnetism in functional materials. While in qualitative agreement with the observed dynamics in experiments, the theoretically predicted magnetic field strengths of circularly polarized phonon modes lack three orders of magnitude. In this work, we put forward a coupling mechanism based on electron-nuclear quantum geometry. This effect is rooted in the adiabatic evolution of the electronic wavefunction under a circular evolution of nuclear coordinates. The excitation pulse then induces a transient level splitting between electron orbitals that carry angular momentum. When converted to effective magnetic fields, values on the order of tens of Teslas are easily reached. We give criteria under which the evolution of nuclear degrees of freedom can be described adiabatically in the electronic sector and find that in the perovskite Strontium Titanate, the adiabatic regime is in experimental reach.   

Multipole Representations of Spin-splitting Terms in Non-magnetic Materials

The band structures of non-centrosymmetric non-magnetic materials display relativistic spin-splitting, rendering them promising candidates for electrically controllable spintronic devices due to spin-momentum locking. While common lowest order terms have been studied in detail, higher-order terms remain little explored. In this study, starting from a centrosymmetric cubic point group, we classify all possible spin-splitting terms using irreducible representations (irreps), identifying terms that go beyond the commonly studied linear Rashba and Dresselhaus effects. We elucidate the connection between spin-orbit coupling terms and electric multipoles or toroidal moments, establishing the different lattice distortion patterns that give rise to the same multipoles. We also perform first-principles density functional theory (DFT) calculations on select materials to quantify the magnitude of the spin-splitting for each lattice distortion pattern.   

Electric, magnetic and toroidal polarizations in crystals

Electric and magnetic multipolar order in bulk crystalline solids is characterized by multipole densities that cannot be cleanly defined using the concepts of classical electromagnetism. We use group theory to overcome this difficulty and present a systematic study of electric, magnetic and toroidal multipolar order in crystalline solids [1]. Based on our symmetry analysis, we identify five categories of polarized matter that provide a complete classification of multipolar order in crystals, including insulators and metals. Each category is characterized by distinct features in the electronic band structure. For example, Rashba spin splitting in electropolar materials like wurtzite represents an electric dipolarization, while Dresselhaus spin splitting in zincblende represents an electric octupolarization. We also develop a general formalism of indicators for individual multipole densities that quantify electric and magnetic multipolar order. Our work clarifies the relation between patterns of localized multipoles and macroscopic multipole densities they give rise to. To illustrate the general theory, we discuss its application to multipole-ordered variants of hexagonal lonsdaleite and cubic diamond. Our work provides a general framework for classifying and expanding current understanding of multipolar order in complex materials.   

Spin space group and quasi-symmetry In Mn3Sn

Mn3Sn is a non-collinear antiferromagnetic material with a kagome structure. Notably, it exhibits a substantial room-temperature anomalous Hall effect (AHE). Recent Density Functional Theory (DFT) calculations have revealed that in the absence of spin-orbit coupling (SOC), a Weyl nodal line exists near the Fermi surface along K-H, and SOC only introduces a small gap with 0.3 Mev. In our study, we have developed an effective Hamiltonian near the K point based on the spin space group of Mn3Sn. It is important to note that, in the absence of SOC, the spin space group, rather than the magnetic space group, accurately describes the symmetry of Mn3Sn. Our effective model matches the DFT results and confirms the the Weyl nodal line is protected by the spin space group. Furthermore, we demonstrate that SOC acts as a secondary perturbation, so that there is a quasi-symmetry protecting the Weyl nodal line. Additionally, we illustrate that out-of-plane spin canting induced by a magnetic field can open the Weyl nodal line and induce Berry curvature, thereby giving rise to in-plane Hall responses. Our work elucidates the application of the spin space group in the study of magnetic topological materials."   

Giant piezoelectricity driven by Thouless pump in conjugated polymers

Thanks to the possibility they offer to convert mechanical energy into electrical energy and vice-versa, piezoelectric materials are of great interest in various fields and find many technological applications, ranging from macro- to microscopic electromechanical devices, to energy harvesting and much more. For their high electromechanical response, the most widely used piezoelectric materials are inorganic perovskites, such as lead zirconate titanate (PZT). However, they present some limitations since they have very low mechanical flexibility, high fabrication costs and are often toxic and not bio-compatible. A promising alternative to overcome these limitations is to exploit piezoelectric properties of organic polymers.

While most organic piezoelectrics rely on the presence of intrinsic local dipoles, a highly nonlocal electronic polarization can be foreseen in conjugated polymers, characterised by delocalized and highly responsive π-electrons. These 1D systems represent a physical realization of a Thouless pump, a mechanism of adiabatic charge transport of topological nature which results, as shown in our work, in anomalously large effective charges, inversely proportional to the band gap energy. A structural (ferroelectric) phase transition further contributes to an enhancement of the piezoelectric response reminiscent of that observed in piezoelectric perovskites close to morphotropic phase boundaries. First-principles Density Functional Theory (DFT) calculations performed in two representative conjugated polymers using hybrid functionals, show that state-of-the-art organic piezoelectric are outperformed by piezoelectric conjugated polymers, mostly thanks to strongly anomalous effective charges of carbon, larger than 5e – ordinary values being of the order of 1e – and reaching the giant value of 30e for band gaps of the order of 1 eV.